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  <div class="section" id="numpy-ufunc-outer">
<h1>numpy.ufunc.outer<a class="headerlink" href="#numpy-ufunc-outer" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.ufunc.outer">
<code class="sig-prename descclassname">ufunc.</code><code class="sig-name descname">outer</code><span class="sig-paren">(</span><em class="sig-param">A</em>, <em class="sig-param">B</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.ufunc.outer" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply the ufunc <em class="xref py py-obj">op</em> to all pairs (a, b) with a in <em class="xref py py-obj">A</em> and b in <em class="xref py py-obj">B</em>.</p>
<p>Let <code class="docutils literal notranslate"><span class="pre">M</span> <span class="pre">=</span> <span class="pre">A.ndim</span></code>, <code class="docutils literal notranslate"><span class="pre">N</span> <span class="pre">=</span> <span class="pre">B.ndim</span></code>. Then the result, <em class="xref py py-obj">C</em>, of
<code class="docutils literal notranslate"><span class="pre">op.outer(A,</span> <span class="pre">B)</span></code> is an array of dimension M + N such that:</p>
<div class="math">
<p><img src="../../_images/math/8b9b3217f67c044047666c17d57fa738cb2adafd.svg" alt="C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =
op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])"/></p>
</div><p>For <em class="xref py py-obj">A</em> and <em class="xref py py-obj">B</em> one-dimensional, this is equivalent to:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">r</span> <span class="o">=</span> <span class="n">empty</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">),</span><span class="nb">len</span><span class="p">(</span><span class="n">B</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">)):</span>
    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">B</span><span class="p">)):</span>
        <span class="n">r</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">B</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="c1"># op = ufunc in question</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A</strong><span class="classifier">array_like</span></dt><dd><p>First array</p>
</dd>
<dt><strong>B</strong><span class="classifier">array_like</span></dt><dd><p>Second array</p>
</dd>
<dt><strong>kwargs</strong><span class="classifier">any</span></dt><dd><p>Arguments to pass on to the ufunc. Typically <a class="reference internal" href="numpy.dtype.html#numpy.dtype" title="numpy.dtype"><code class="xref py py-obj docutils literal notranslate"><span class="pre">dtype</span></code></a> or <em class="xref py py-obj">out</em>.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>r</strong><span class="classifier">ndarray</span></dt><dd><p>Output array</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="numpy.outer.html#numpy.outer" title="numpy.outer"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.outer</span></code></a></p>
</div>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="o">.</span><span class="n">outer</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">])</span>
<span class="go">array([[ 4,  5,  6],</span>
<span class="go">       [ 8, 10, 12],</span>
<span class="go">       [12, 15, 18]])</span>
</pre></div>
</div>
<p>A multi-dimensional example:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(2, 3)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">B</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(1, 4)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">shape</span><span class="p">;</span> <span class="n">C</span>
<span class="go">(2, 3, 1, 4)</span>
<span class="go">array([[[[ 1,  2,  3,  4]],</span>
<span class="go">        [[ 2,  4,  6,  8]],</span>
<span class="go">        [[ 3,  6,  9, 12]]],</span>
<span class="go">       [[[ 4,  8, 12, 16]],</span>
<span class="go">        [[ 5, 10, 15, 20]],</span>
<span class="go">        [[ 6, 12, 18, 24]]]])</span>
</pre></div>
</div>
</dd></dl>

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